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Testing the Bethe ansatz with large N renormalons
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abstract
The ground state energy of integrable asymptotically free theories can be conjecturally computed by using the Bethe ansatz, once the theory has been coupled to an external potential through a conserved charge. This leads to a precise prediction for the perturbative expansion of the energy. We provide a non-trivial test of this prediction in the non-linear sigma model and its supersymmetric extension, by calculating analytically the associated Feynman diagrams at next-to-leading order in the $1/N$ expansion, and at all loops. By investigating the large order behaviour of the diagrams, we locate the position of the renormalons of the theory and we obtain an analytic expression for the large $N$ trans-series associated to each. As a spin-off of our calculation, we provide a direct derivation of the beta function of these theories, at next-to-leading order in the $1/N$ expansion.
Forward citations
Cited by 2 Pith papers
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Renormalon-like factorial enhancements to power expansion/OPE in a super-renormalizable 2D $O(N)$ quartic model
In the 2D large-N O(N) quartic model, the large-momentum OPE of the scalar two-point function is divergent: coefficient functions and operator condensates carry n! factorial growths that cancel only off-diagonally, ne...
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The complete trans-series for conserved charges in integrable field theories
A unified Wiener-Hopf construction gives all-order trans-series for conserved charges in O(N), SU(N), Lieb-Liniger, Gaudin-Yang and capacitor models, with numerically checked Borel resummation.
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